OP497GSZ Datasheet, PDF (13/16 Pages) Analog Devices – Precision Picoampere Input Current Quad Operational Amplifier

NONLINEAR CIRCUITS
Due to its low input bias currents, the OP497 is an ideal log
amplifier in nonlinear circuits, such as the squaring amplifier
and square root amplifier circuits shown in Figure 40 and
Figure 41. Using the squaring amplifier circuit in Figure 40
as an example, the analysis begins by writing a voltage loop
equation across Transistors Q1, Q2, Q3, and Q4.
V_T1In_{⎜⎜⎝⎛}
I_IN
I_S1
⎟⎟⎠⎞
+
V_T2In_{⎜⎜⎝⎛}
I_IN
I_S2
⎟⎟⎠⎞
=
V_T3In_{⎜⎜⎝⎛}
I
I_O
I_S3
⎟⎟⎠⎞
+
V_T4In_{⎜⎜⎝⎛}
I_REF
I_S4
⎟⎟⎠⎞
All the transistors in the MAT04 are precisely matched and at
the same temperature; therefore, the IS and VT terms cancel,
giving
2InIIN = InIO + InIREF = In (IO × IREF)
Exponentiating both sides of the thick equation lead to
( ) _{IO =}
I_IN ²
I _REF
Op amp A2 forms a current-to-voltage converter which results
in VOUT = R2 × IO. Substituting (VIN/R1) for IIN and the previous
equation for IO yields
V_OUT
=
⎜⎜⎝⎛
R2
I _REF
⎟⎟⎠⎞
⎜⎛
⎝
V_IN
R1
⎟⎞ ²
⎠
C2
100pF
R1
133kΩ ^IIN
V_IN
R2
6 ^{A2 33kΩ}
1
1/4
7
I_O
OP497
5
V_OUT
2 _Q1
3
7
6
Q2
V+ C1
A1
100pF
2
8
1/4
1
OP497
3
4
5
MAT04
8
Q3 ⁹
10
14
I_REF Q4 ¹³
12
R3
50kΩ
R4
50kΩ
V–
–15V
Figure 40. Squaring Amplifier
OP497
A similar analysis made for the square root amplifier circuit in
Figure 41 leads to its transfer function
V_OUT = R2
(V_IN )(I _REF )
R1
In these circuits, IREF is a function of the negative power supply. To
maintain accuracy, the negative supply should be well regulated.
For applications where very high accuracy is required, a voltage
reference can be used to set IREF. An important consideration for
the squaring circuit is that a sufficiently large input voltage can
force the output beyond the operating range of the output op
amp. Resistor R4 can be changed to scale IREF, or R1 and R2 can
be varied to keep the output voltage within the usable range.
R2
33kΩ
C2
6
100pF
1/4
7
I_{O OP497}
5
V_OUT
R1
33kΩ
V_IN
I_IN
C1
100pF
V+
2
8
1/4
1
OP497
3
4
Q1 1 _MAT04
2
I_REF
3
7
6 _Q2
14
13
Q4
8
12
Q3 ⁹
5 10
R5
2kΩ
R3
50kΩ
R4
50kΩ
V–
–15V
Figure 41. Square Root Amplifier
Unadjusted accuracy of the square root circuit is better than
0.1% over an input voltage range of 100 mV to 10 V. For a similar
input voltage range, the accuracy of the squaring circuit is better
than 0.5%.
Rev. E | Page 13 of 16